Noise in simulating logistic regression model

Asked Oct 12 '21 at 18:40

Active Oct 12 '21 at 18:51

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I would like to simulate data for logistic regression model as follows,

X = rnorm(1000)
Z = 1 + 2*X
pr = 1/(1 + exp(-Z))
Y = rbinom(1000, 1, pr)
glm(Y ~ X, family="binomial")

I am just wondering, in the step of generating "pr", do I need to add a noise to Z? It seems there is no noise added to Y to fit a logistic regression model. In other words, should I write Z = 1 + 2X or Z = 1 + 2X + rnorm(1000)?

edited Oct 12 '21 at 18:51

whuber

322,774

asked Oct 12 '21 at 18:40

Phoebe

5

rbinom is your "noise" generator. The model is conditional on X, so adding noise to Z is not part of the model. – whuber Oct 12 '21 at 18:50
2

Why do we model noise in linear regression but not logistic regression? approaches this question "from the other side" but may be helpful. – Stephan Kolassa Oct 12 '21 at 20:40

Noise in simulating logistic regression model

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